/*    $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $    */
/*    $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
/* $FreeBSD: releng/11.2/sys/sys/tree.h 331722 2018-03-29 02:50:57Z eadler $  */

/*-
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef    _SYS_TREE_H_
#define    _SYS_TREE_H_

#include <sys/cdefs.h>

#ifdef __cplusplus
#if __cplusplus
extern "C" {
#endif /* __cplusplus */
#endif /* __cplusplus */
/*
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *    - every search path from the root to a leaf consists of the
 *      same number of black nodes,
 *    - each red node (except for the root) has a black parent,
 *    - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)                        \
struct name {                                \
    struct type *rbh_root; /* root of the tree */            \
}

#define RB_INITIALIZER(root)                        \
    { NULL }

#define RB_INIT(root) do {                        \
    (root)->rbh_root = NULL;                    \
} while (/*CONSTCOND*/ 0)

#define RB_BLACK    0
#define RB_RED        1
#define RB_ENTRY(type)                            \
struct {                                \
    struct type *rbe_left;        /* left element */        \
    struct type *rbe_right;        /* right element */        \
    struct type *rbe_parent;    /* parent element */        \
    int rbe_color;            /* node color */        \
}

#define RB_LEFT(elm, field)        (elm)->field.rbe_left
#define RB_RIGHT(elm, field)        (elm)->field.rbe_right
#define RB_PARENT(elm, field)        (elm)->field.rbe_parent
#define RB_COLOR(elm, field)        (elm)->field.rbe_color
#define RB_ROOT(head)            (head)->rbh_root
#define RB_EMPTY(head)            (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) do {                    \
    RB_PARENT(elm, field) = parent;                    \
    RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;        \
    RB_COLOR(elm, field) = RB_RED;                    \
} while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) do {                \
    RB_COLOR(black, field) = RB_BLACK;                \
    RB_COLOR(red, field) = RB_RED;                    \
} while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x)    do {} while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) do {            \
    (tmp) = RB_RIGHT(elm, field);                    \
    if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {    \
        RB_PARENT(RB_LEFT(tmp, field), field) = (elm);        \
    }                                \
    RB_AUGMENT(elm);                        \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {    \
        if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))    \
            RB_LEFT(RB_PARENT(elm, field), field) = (tmp);    \
        else                            \
            RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);    \
    } else                                \
        (head)->rbh_root = (tmp);                \
    RB_LEFT(tmp, field) = (elm);                    \
    RB_PARENT(elm, field) = (tmp);                    \
    RB_AUGMENT(tmp);                        \
    if ((RB_PARENT(tmp, field)))                    \
        RB_AUGMENT(RB_PARENT(tmp, field));            \
} while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {            \
    (tmp) = RB_LEFT(elm, field);                    \
    if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {    \
        RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);        \
    }                                \
    RB_AUGMENT(elm);                        \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {    \
        if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))    \
            RB_LEFT(RB_PARENT(elm, field), field) = (tmp);    \
        else                            \
            RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);    \
    } else                                \
        (head)->rbh_root = (tmp);                \
    RB_RIGHT(tmp, field) = (elm);                    \
    RB_PARENT(elm, field) = (tmp);                    \
    RB_AUGMENT(tmp);                        \
    if ((RB_PARENT(tmp, field)))                    \
        RB_AUGMENT(RB_PARENT(tmp, field));            \
} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define    RB_PROTOTYPE(name, type, field, cmp)                \
    RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
#define    RB_PROTOTYPE_STATIC(name, type, field, cmp)            \
    RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)        \
    RB_PROTOTYPE_INSERT_COLOR(name, type, attr);            \
    RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);            \
    RB_PROTOTYPE_REMOVE(name, type, attr);                \
    RB_PROTOTYPE_NEXT(name, type, attr);                \
    RB_PROTOTYPE_PREV(name, type, attr);             \
    RB_PROTOTYPE_MINMAX(name, type, attr);
#define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)            \
    attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
#define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)            \
    attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
#define RB_PROTOTYPE_REMOVE(name, type, attr)                \
    attr struct type *name##_RB_REMOVE(struct name *, struct type *)
#define RB_PROTOTYPE_NEXT(name, type, attr)                \
    attr struct type *name##_RB_NEXT(struct type *)
#define RB_PROTOTYPE_PREV(name, type, attr)                \
    attr struct type *name##_RB_PREV(struct type *)
#define RB_PROTOTYPE_MINMAX(name, type, attr)                           \
        attr struct type *name##_RB_MINMAX(struct name *, int)

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define    RB_GENERATE(name, type, field, cmp)                \
    RB_GENERATE_INTERNAL(name, type, field, cmp,)
#define    RB_GENERATE_STATIC(name, type, field, cmp)            \
    RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)        \
    RB_GENERATE_INSERT_COLOR(name, type, field, attr)        \
    RB_GENERATE_REMOVE_COLOR(name, type, field, attr)        \
    RB_GENERATE_REMOVE(name, type, field, attr)            \
    RB_GENERATE_NEXT(name, type, field, attr)            \
    RB_GENERATE_PREV(name, type, field, attr)            \
    RB_GENERATE_MINMAX(name, type, field, attr)

#define RB_GENERATE_INSERT_COLOR(name, type, field, attr)        \
attr void                                \
name##_RB_INSERT_COLOR(struct name *head, struct type *elm)        \
{                                    \
    struct type *parent, *gparent, *tmp;                \
    while ((parent = RB_PARENT(elm, field)) != NULL &&        \
        RB_COLOR(parent, field) == RB_RED) {            \
        gparent = RB_PARENT(parent, field);            \
        if (parent == RB_LEFT(gparent, field)) {        \
            tmp = RB_RIGHT(gparent, field);            \
            if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
                RB_COLOR(tmp, field) = RB_BLACK;    \
                RB_SET_BLACKRED(parent, gparent, field);\
                elm = gparent;                \
                continue;                \
            }                        \
            if (RB_RIGHT(parent, field) == elm) {        \
                RB_ROTATE_LEFT(head, parent, tmp, field);\
                tmp = parent;                \
                parent = elm;                \
                elm = tmp;                \
            }                        \
            RB_SET_BLACKRED(parent, gparent, field);    \
            RB_ROTATE_RIGHT(head, gparent, tmp, field);    \
        } else {                        \
            tmp = RB_LEFT(gparent, field);            \
            if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
                RB_COLOR(tmp, field) = RB_BLACK;    \
                RB_SET_BLACKRED(parent, gparent, field);\
                elm = gparent;                \
                continue;                \
            }                        \
            if (RB_LEFT(parent, field) == elm) {        \
                RB_ROTATE_RIGHT(head, parent, tmp, field);\
                tmp = parent;                \
                parent = elm;                \
                elm = tmp;                \
            }                        \
            RB_SET_BLACKRED(parent, gparent, field);    \
            RB_ROTATE_LEFT(head, gparent, tmp, field);    \
        }                            \
    }                                \
    RB_COLOR(head->rbh_root, field) = RB_BLACK;            \
}

#define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)        \
attr void                                \
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{                                    \
    struct type *tmp;                        \
    while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&    \
        elm != RB_ROOT(head)) {                    \
        if (RB_LEFT(parent, field) == elm) {            \
            tmp = RB_RIGHT(parent, field);            \
            if (RB_COLOR(tmp, field) == RB_RED) {        \
                RB_SET_BLACKRED(tmp, parent, field);    \
                RB_ROTATE_LEFT(head, parent, tmp, field);\
                tmp = RB_RIGHT(parent, field);        \
            }                        \
            if ((RB_LEFT(tmp, field) == NULL ||        \
                RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
                (RB_RIGHT(tmp, field) == NULL ||        \
                RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
                RB_COLOR(tmp, field) = RB_RED;        \
                elm = parent;                \
                parent = RB_PARENT(elm, field);        \
            } else {                    \
                if (RB_RIGHT(tmp, field) == NULL ||    \
                    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
                    struct type *oleft;        \
                    if ((oleft = RB_LEFT(tmp, field)) \
                        != NULL)            \
                        RB_COLOR(oleft, field) = RB_BLACK;\
                    RB_COLOR(tmp, field) = RB_RED;    \
                    RB_ROTATE_RIGHT(head, tmp, oleft, field);\
                    tmp = RB_RIGHT(parent, field);    \
                }                    \
                RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
                RB_COLOR(parent, field) = RB_BLACK;    \
                if (RB_RIGHT(tmp, field))        \
                    RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
                RB_ROTATE_LEFT(head, parent, tmp, field);\
                elm = RB_ROOT(head);            \
                break;                    \
            }                        \
        } else {                        \
            tmp = RB_LEFT(parent, field);            \
            if (RB_COLOR(tmp, field) == RB_RED) {        \
                RB_SET_BLACKRED(tmp, parent, field);    \
                RB_ROTATE_RIGHT(head, parent, tmp, field);\
                tmp = RB_LEFT(parent, field);        \
            }                        \
            if ((RB_LEFT(tmp, field) == NULL ||        \
                RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
                (RB_RIGHT(tmp, field) == NULL ||        \
                RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
                RB_COLOR(tmp, field) = RB_RED;        \
                elm = parent;                \
                parent = RB_PARENT(elm, field);        \
            } else {                    \
                if (RB_LEFT(tmp, field) == NULL ||    \
                    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
                    struct type *oright;        \
                    if ((oright = RB_RIGHT(tmp, field)) \
                        != NULL)            \
                        RB_COLOR(oright, field) = RB_BLACK;\
                    RB_COLOR(tmp, field) = RB_RED;    \
                    RB_ROTATE_LEFT(head, tmp, oright, field);\
                    tmp = RB_LEFT(parent, field);    \
                }                    \
                RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
                RB_COLOR(parent, field) = RB_BLACK;    \
                if (RB_LEFT(tmp, field))        \
                    RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
                RB_ROTATE_RIGHT(head, parent, tmp, field);\
                elm = RB_ROOT(head);            \
                break;                    \
            }                        \
        }                            \
    }                                \
    if (elm)                            \
        RB_COLOR(elm, field) = RB_BLACK;            \
}

#define RB_GENERATE_REMOVE(name, type, field, attr)            \
attr struct type *                            \
name##_RB_REMOVE(struct name *head, struct type *elm)            \
{                                    \
    struct type *child, *parent, *old = elm;            \
    int color;                            \
    if (RB_LEFT(elm, field) == NULL)                \
        child = RB_RIGHT(elm, field);                \
    else if (RB_RIGHT(elm, field) == NULL)                \
        child = RB_LEFT(elm, field);                \
    else {                                \
        struct type *left;                    \
        elm = RB_RIGHT(elm, field);                \
        while ((left = RB_LEFT(elm, field)) != NULL)        \
            elm = left;                    \
        child = RB_RIGHT(elm, field);                \
        parent = RB_PARENT(elm, field);                \
        color = RB_COLOR(elm, field);                \
        if (child)                        \
            RB_PARENT(child, field) = parent;        \
        if (parent) {                        \
            if (RB_LEFT(parent, field) == elm)        \
                RB_LEFT(parent, field) = child;        \
            else                        \
                RB_RIGHT(parent, field) = child;    \
            RB_AUGMENT(parent);                \
        } else                            \
            RB_ROOT(head) = child;                \
        if (RB_PARENT(elm, field) == old)            \
            parent = elm;                    \
        (elm)->field = (old)->field;                \
        if (RB_PARENT(old, field)) {                \
            if (RB_LEFT(RB_PARENT(old, field), field) == old)\
                RB_LEFT(RB_PARENT(old, field), field) = elm;\
            else                        \
                RB_RIGHT(RB_PARENT(old, field), field) = elm;\
            RB_AUGMENT(RB_PARENT(old, field));        \
        } else                            \
            RB_ROOT(head) = elm;                \
        RB_PARENT(RB_LEFT(old, field), field) = elm;        \
        if (RB_RIGHT(old, field))                \
            RB_PARENT(RB_RIGHT(old, field), field) = elm;    \
        if (parent) {                        \
            left = parent;                    \
            do {                        \
                RB_AUGMENT(left);            \
            } while ((left = RB_PARENT(left, field)) != NULL); \
        }                            \
        goto color;                        \
    }                                \
    parent = RB_PARENT(elm, field);                    \
    color = RB_COLOR(elm, field);                    \
    if (child)                            \
        RB_PARENT(child, field) = parent;            \
    if (parent) {                            \
        if (RB_LEFT(parent, field) == elm)            \
            RB_LEFT(parent, field) = child;            \
        else                            \
            RB_RIGHT(parent, field) = child;        \
        RB_AUGMENT(parent);                    \
    } else                                \
        RB_ROOT(head) = child;                    \
color:                                    \
    if (color == RB_BLACK)                        \
        name##_RB_REMOVE_COLOR(head, parent, child);        \
    return (old);                            \
}                                    \

#define RB_GENERATE_NEXT(name, type, field, attr)            \
/* ARGSUSED */                                \
attr struct type *                            \
name##_RB_NEXT(struct type *elm)                    \
{                                    \
    if (RB_RIGHT(elm, field)) {                    \
        elm = RB_RIGHT(elm, field);                \
        while (RB_LEFT(elm, field))                \
            elm = RB_LEFT(elm, field);            \
    } else {                            \
        if (RB_PARENT(elm, field) &&                \
            (elm == RB_LEFT(RB_PARENT(elm, field), field)))    \
            elm = RB_PARENT(elm, field);            \
        else {                            \
            while (RB_PARENT(elm, field) &&            \
                (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
                elm = RB_PARENT(elm, field);        \
            elm = RB_PARENT(elm, field);            \
        }                            \
    }                                \
    return (elm);                            \
}

#define RB_GENERATE_PREV(name, type, field, attr)            \
/* ARGSUSED */                                \
attr struct type *                            \
name##_RB_PREV(struct type *elm)                    \
{                                    \
    if (RB_LEFT(elm, field)) {                    \
        elm = RB_LEFT(elm, field);                \
        while (RB_RIGHT(elm, field))                \
            elm = RB_RIGHT(elm, field);            \
    } else {                            \
        if (RB_PARENT(elm, field) &&                \
            (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
            elm = RB_PARENT(elm, field);            \
        else {                            \
            while (RB_PARENT(elm, field) &&            \
                (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
                elm = RB_PARENT(elm, field);        \
            elm = RB_PARENT(elm, field);            \
        }                            \
    }                                \
    return (elm);                            \
}

#define RB_GENERATE_MINMAX(name, type, field, attr)            \
attr struct type *                            \
name##_RB_MINMAX(struct name *head, int val)                \
{                                    \
    struct type *tmp = RB_ROOT(head);                \
    struct type *parent = NULL;                    \
    while (tmp) {                            \
        parent = tmp;                        \
        if (val < 0)                        \
            tmp = RB_LEFT(tmp, field);            \
        else                            \
            tmp = RB_RIGHT(tmp, field);            \
    }                                \
    return (parent);                        \
}


#define RB_NEGINF    -1
#define RB_INF    1

#define RB_NEXT(name, x, y)    name##_RB_NEXT(y)
#define RB_PREV(name, x, y)    name##_RB_PREV(y)
#define RB_MIN(name, x)        name##_RB_MINMAX(x, RB_NEGINF)

#ifdef __cplusplus
#if __cplusplus
}
#endif /* __cplusplus */
#endif /* __cplusplus */

#endif    /* _SYS_TREE_H_ */
